How do you make an image emission without washing out the image?
You might want to learn how the view transform impacts the dynamic range of capture.

Using color management and custom LUTs you can work using a much higher dynamic range. Using simple shaders you can do things like this, where no other lights are used on the scene, just the image on the TV screen.:



See:

Make the flame of a candle more yellow

Render with a wider dynamic range in cycles to produce photorealistic looking images